When digitally synthesising a waveform various digital values are read out from a memory and are filtered to produce an analogue waveform which is transmitted through an air interface or through a landline, such as a co-axial cable or optical fibre.
An analogue filter for doing this task can be problematic and implementing the desired filtering characteristic using a digital filter is relatively costly and has limits on its operational speed due to the number of multiplications involved.
European Patent Specification EP 0 132 988 B1 discloses an implementation of a digital synthesis technique for a precisely controlled waveform having predetermined time and frequency characteristics in response to a binary input data stream. More particularly a truncated impulse response is stored and each transmission symbol provides a weighting for its component of the impulse response. Collectively each currently transmitted symbol is a function of the weighting assigned to its impulse function plus the weighting assigned to each neighbouring impulse function by the value of their respective transmission symbol states. Finally, the amount contributed from an impulse response of a neighbouring transmission symbol must take into account its temporal relationship, or time displacement, from the current transmission symbol. This patent specification discloses a number of embodiments of which a first, FIG. 1, relates to a 16 quadrature amplitude modulation signal using 4-level signals and a truncated sequence of 9 impulse responses which requires 4.sup.9 (or 262144) addressable memory locations. Another embodiment, FIG. 8, reduces this number of addressable memory locations by means of partial summations where each term is made up of the sum of three corresponding terms in some equations given. As a result each partial sum requires fewer addresses (hence less memory). In the example given six ROMs, each requiring 64 memory locations, accomplish the same memory function as two ROMs each requiring 2.sup.9 memory locations.